Image pattern recognition with Mahalanobis & Euclidean distances

Luiz Eduardo Pizzinatto

&

Bruno Martins Crocomo

python Main.py

• Load an image
• Select (in that image square) a small pattern color to recognize (change radius for thicker/larger lines)
• Define any threshold (between 0 and 255)
• Choose any distance as Mahalanobis or Euclidean
• Press test
• Check average color value, play with threshold and re-test to check new results

Two tests bellow, selecting some forehead pixels as pattern. As you can see, Mahalanobis distance is more accurate to detect the same pattern.

Two tests bellow, selecting some black tshirt pixels. Again, Mahalanobis distance is more accurate than Euclidean distance.

From the small pattern selected (a couple of pixels), the covariance inverse matrix is calculated from each pixel RED, GREEN and BLUE components. Hence, Mahalanobis distance is made as follows:

	distance = (x-y) * A^(-1) * (x-y)T

where:

    x is the element we want to discover the distance (with its own RED, GREEN, BLUE values)
    y is the average basis element, (i.e. an element with average RED, GREEN, BLUE value  from all selected patterns)
    A^(-1) is the covariance inverse matrix from the selected patterns

This distance was normalized as:

	norm = exp(-distance) * 255

The multiplication by 255 was made to generate a gray scale.

As small distances generate large normalized values and when RGB components become more white when near to 255, then distance is used as -distance. The value was inverted so that samples with small distances become darker and larger distances become whiter.

This was made as being the distance between each pixel from original image in relation to average center of patterns, without windowing.